{"product_id":"2940016537061","title":"The Number System of Algebra: Number Systems from the Egyptians to the Greeks to the Europeans to Arabic","description":"I THEORETICAL\u003cbr\u003e1  THE POSITIVE INTEGER,\u003cbr\u003e AND THE LAWS WHICH REGULATE THE ADDITION AND\u003cbr\u003e MULTIPLICATION OF POSITIVE INTEGERS\u003cbr\u003e The number concept \u003cbr\u003e Numerical equality \u003cbr\u003e Numeral symbols \u003cbr\u003e The numerical equation \u003cbr\u003e Counting \u003cbr\u003e Addition and its laws \u003cbr\u003e Multiplication and its laws \u003cbr\u003e\u003cbr\u003e2  SUBTRACTION AND THE NEGATIVE INTEGER\u003cbr\u003e Numerical subtraction \u003cbr\u003e Determinateness of numerical subtraction \u003cbr\u003e Formal rules of subtraction \u003cbr\u003e Limitations of numerical subtraction \u003cbr\u003e Symbolic equations \u003cbr\u003e Principle of permanence.  Symbolic subtraction \u003cbr\u003e Zero \u003cbr\u003e The negative \u003cbr\u003e Recapitulation of the argument of the chapter \u003cbr\u003e\u003cbr\u003e3  DIVISION AND THE FRACTION\u003cbr\u003e Numerical division \u003cbr\u003e Determinateness of numerical division \u003cbr\u003e Formal rules of division \u003cbr\u003e Limitations of numerical division \u003cbr\u003e Symbolic division.  The fraction \u003cbr\u003e Negative fractions \u003cbr\u003e General test of the equality or inequality of fractions \u003cbr\u003e Indeterminateness of division by zero \u003cbr\u003e Determinateness of symbolic division \u003cbr\u003e The vanishing of a product \u003cbr\u003e The system of rational numbers \u003cbr\u003e\u003cbr\u003e4  THE IRRATIONAL\u003cbr\u003e Inadequateness of the system of rational numbers \u003cbr\u003e Numbers defined by regular sequences.   The irrational\u003cbr\u003e Generalized definitions of zero, positive, negative \u003cbr\u003e Of the four fundamental operations \u003cbr\u003e Of equality and greater and lesser inequality \u003cbr\u003e The number defined by a regular sequence its limiting value \u003cbr\u003e Division by zero \u003cbr\u003e The number-system defined by regular sequences of rationals a closed and continuous system \u003cbr\u003e  \u003cbr\u003e5  THE IMAGINARY  COMPLEX NUMBERS\u003cbr\u003e The pure imaginary \u003cbr\u003e Complex numbers \u003cbr\u003e The fundamental operations on complex numbers \u003cbr\u003e Numerical comparison of complex numbers \u003cbr\u003e Adequateness of the system of complex number \u003cbr\u003e Fundamental characteristics of the algebra of number \u003cbr\u003e \u003cbr\u003e6  GRAPHICAL REPRESENTATION OF NUMBERS  THE VARIABLE.\u003cbr\u003e Correspondence between the real number-system and the points of a line\u003cbr\u003e The continuous variable \u003cbr\u003e Correspondence between the complex number-system and the points of a plane\u003cbr\u003e The complex variable \u003cbr\u003e Definitions of modulus and argument of a complex number and of sine,\u003cbr\u003e cosine, and circular measure of an angle \u003cbr\u003e Demonstration that a + ib = ½(cos µ + i sin µ) = ½eiµ \u003cbr\u003e Construction of the points which represent the sum, difference, product,\u003cbr\u003e and quotient of two complex numbers \u003cbr\u003e \u003cbr\u003e7  THE FUNDAMENTAL THEOREM OF ALGEBRA\u003cbr\u003e Definitions of the algebraic equation and its roots \u003cbr\u003e Demonstration that an algebraic equation of the nth degree has n roots \u003cbr\u003e \u003cbr\u003e8 INFINITE SERIES\u003cbr\u003e8.1 REAL SERIES\u003cbr\u003e Definitions of sum, convergence, and divergence \u003cbr\u003e General test of convergence \u003cbr\u003e Absolute and conditional convergence \u003cbr\u003e Special tests of convergence \u003cbr\u003e Limits of convergence \u003cbr\u003e The fundamental operations on infinite series \u003cbr\u003e8.2 COMPLEX SERIES\u003cbr\u003e General test of convergence \u003cbr\u003e Absolute and conditional convergence \u003cbr\u003e The region of convergence \u003cbr\u003e A theorem respecting complex series \u003cbr\u003e The fundamental operations on complex series \u003cbr\u003e \u003cbr\u003e9  THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS UNDETERMINED COEFFICIENTS. INVOLUTION AND EVOLUTION. THE BINOMIAL THEOREM\u003cbr\u003e Definition of function \u003cbr\u003e Functional equation of the exponential function \u003cbr\u003e Undetermined coefficients \u003cbr\u003e The exponential function \u003cbr\u003e The functions sine and cosine \u003cbr\u003e Periodicity of these functions \u003cbr\u003e The logarithmic function \u003cbr\u003e Indeterminateness of logarithms \u003cbr\u003e Permanence of the laws of exponents \u003cbr\u003e Permanence of the laws of logarithms \u003cbr\u003e Involution and evolution \u003cbr\u003e The binomial theorem for complex exponents \u003cbr\u003e \u003cbr\u003eII HISTORICAL\u003cbr\u003e10  PRIMITIVE NUMERALS\u003cbr\u003e Gesture symbols \u003cbr\u003e Spoken symbols \u003cbr\u003e Written symbols \u003cbr\u003e \u003cbr\u003e11  HISTORIC SYSTEMS OF NOTATION\u003cbr\u003e Egyptian and Phoenician \u003cbr\u003e Greek \u003cbr\u003e Roman \u003cbr\u003e Indo-Arabic \u003cbr\u003e \u003cbr\u003e12  THE FRACTION\u003cbr\u003e Primitive fractions \u003cbr\u003e Roman fractions \u003cbr\u003e Egyptian (the Book of Ahmes) \u003cbr\u003e Babylonian or sexagesimal \u003cbr\u003e Greek \u003cbr\u003e \u003cbr\u003e13  ORIGIN OF THE IRRATIONAL\u003cbr\u003e Discovery of irrational lines.  Pythagoras \u003cbr\u003e Consequences of this discovery in Greek mathematics \u003cbr\u003e Greek approximate values of irrationals \u003cbr\u003e \u003cbr\u003e14  ORIGIN OF THE NEGATIVE AND THE IMAGINARY.\u003cbr\u003e15  ACCEPTANCE OF THE NEGATIVE\u003cbr\u003e16  RECOGNITION OF THE PURELY SYMBOLIC CHARACTERS OF ALGEBRA","brand":"Fine","offers":[{"title":"Default Title","offer_id":47172105273584,"sku":"2940016537061","price":2.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940016537061_p0.jpg?v=1763656501","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940016537061","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}